AP Notes Chapter 6 Atomic Structure Describe properties of electromagnetic radiation Describe properties of electromagnetic radiation Light & relationship to atomic structure Light & relationship to atomic structure Wave-particle duality Wave-particle duality Basic ideas of quantum mechanics Basic ideas of quantum mechanics Quantum numbers & atomic structure Quantum numbers & atomic structure

Electromagnetic Spectrum

Light Made up of electromagnetic radiation. Made up of electromagnetic radiation. Waves of electric and magnetic fields at right angles to each other. Waves of electric and magnetic fields at right angles to each other. Parts of a wave Wavelength Frequency ( ) = number of cycles in one second Measured in hertz 1 hertz (hz) = 1 cycle/second

EMR - Wave Nature c = c = where c = Speed of light  = wavelength  = frequency

EMR - Particle Nature (Quantized) Planck: E = h E = energy h = Planck’s constant = x J. s  = frequency

Reminder

Kinds of EM waves There are many different and There are many different and Radio waves, microwaves, x rays and gamma rays are all examples. Radio waves, microwaves, x rays and gamma rays are all examples. Light is only the part our eyes can detect. Light is only the part our eyes can detect. Gamma Rays Radio waves

The speed of light in a vacuum is x 10 8 m/s in a vacuum is x 10 8 m/s = c = c c =  = wavelength x frequency c =  = wavelength x frequency What is the wavelength of light with a frequency 5.89 x 10 5 Hz? What is the wavelength of light with a frequency 5.89 x 10 5 Hz? What is the frequency of blue light with a wavelength of 484 nm? What is the frequency of blue light with a wavelength of 484 nm?

In 1900(s) Matter and energy were seen as different from each other in fundamental ways. Matter and energy were seen as different from each other in fundamental ways. Matter was particles. Matter was particles. Energy could come in waves, with any frequency. Energy could come in waves, with any frequency. Max Planck found that as the cooling of hot objects couldn’t be explained by viewing energy as a wave. Max Planck found that as the cooling of hot objects couldn’t be explained by viewing energy as a wave.

Energy is Quantized Planck found  E came in chunks with size h Planck found  E came in chunks with size h  E = nh or nhc/  E = nh or nhc/ where n is an integer. where n is an integer. and h is Planck’s constant and h is Planck’s constant h = x J s h = x J s these packets of h are called quantum these packets of h are called quantum

Einstein is next Said electromagnetic radiation is quantized in particles called photons. Said electromagnetic radiation is quantized in particles called photons. Each photon has energy = h = hc/ Each photon has energy = h = hc/ Combine this with Einstein’s E = mc 2 Combine this with Einstein’s E = mc 2 You get the apparent mass of a photon. You get the apparent mass of a photon. m = h / ( c) m = h / ( c)

Neils Bohr (1885 –1962) Bohr Model of the Hydrogen Atom

Bohr model of the atom In the Bohr model, electrons can only exist at specific energy levels (orbit). Energy

The Bohr Ring Atom n = 3 n = 4 n = 2 n = 1

Bohr Model of Atom Postulates P1 : e - revolves around the nucleus in a circular orbit orbit

Bohr Model of Atom Postulates P2 : Only orbits allowed are those with angular momentum of integral multiples of:

Bohr Model of Atom Postulates P3 : e - does not radiate energy in orbit, but gains energy to go to higher level allowed orbit & radiates energy when falling to lower orbit

Photo Absorption and Emission

The Bohr Model n is the energy level n is the energy level for each energy level the energy is for each energy level the energy is Z is the nuclear charge, which is +1 for hydrogen. Z is the nuclear charge, which is +1 for hydrogen. E = x J (Z 2 / n 2 ) E = x J (Z 2 / n 2 ) n = 1 is called the ground state n = 1 is called the ground state when the electron is removed, n =  when the electron is removed, n =  E = 0 E = 0

We are worried about the change When the electron moves from one energy level to another. When the electron moves from one energy level to another.  E = E final - E initial  E = E final - E initial  E = x J Z 2 (1/ n f 2 - 1/ n i 2 )  E = x J Z 2 (1/ n f 2 - 1/ n i 2 )

Rotating Object Balance Centrifugal Force = electrical attraction of positive nucleus and negative e - Centrifugal Force = electrical attraction of positive nucleus and negative e -

Centrifugal Force = Electrostatic Attraction

Definition Angular Momentum = mvr Angular Momentum = mvr By P2: By P2:

By rearrangement:

For H-atom [n = 1] r = 5.29 x m or 52.9 pm = Angstoms

In general, when n = orbit a 0 = radius of H-atom for n = 1 & Z = atomic #

To keep e - in orbit, must balance kinetic energy and potential energy

where k = Rydberg constant k = x J

For the transition of an e - from an initial energy level (E i ) to a final energy level (E f ), we can write

Examples Calculate the energy need to move an electron from its to the third energy level. Calculate the energy need to move an electron from its to the third energy level. Calculate the energy released when an electron moves from n= 4 to n=2 in a hydrogen atom. Calculate the energy released when an electron moves from n= 4 to n=2 in a hydrogen atom. Calculate the energy released when an electron moves from n= 5 to n=3 in a He +1 ion Calculate the energy released when an electron moves from n= 5 to n=3 in a He +1 ion

When is it true? Only for hydrogen atoms and other monoelectronic species. Only for hydrogen atoms and other monoelectronic species. Why the negative sign? Why the negative sign? To increase the energy of the electron you make it closer to the nucleus. To increase the energy of the electron you make it closer to the nucleus. the maximum energy an electron can have is zero, at an infinite distance. the maximum energy an electron can have is zero, at an infinite distance.

The Bohr Model Doesn’t work. Doesn’t work. Only works for hydrogen atoms. Only works for hydrogen atoms. Electrons don’t move in circles. Electrons don’t move in circles. The quantization of energy is right, but not because they are circling like planets. The quantization of energy is right, but not because they are circling like planets.

Which is it? Is energy a wave like light, or a particle? Is energy a wave like light, or a particle? Yes Yes Concept is called the Wave-Particle duality. Concept is called the Wave-Particle duality. What about the other way, is matter a wave? What about the other way, is matter a wave? Yes Yes

The Quantum Mechanical Model A totally new approach. A totally new approach. De Broglie said matter could be like a wave. De Broglie said matter could be like a wave. De Broglie said they were like standing waves. De Broglie said they were like standing waves. The vibrations of a stringed instrument. The vibrations of a stringed instrument.

Matter as a wave Using the velocity v instead of the wavelength we get. Using the velocity v instead of the wavelength we get. De Broglie’s equation = h/mv De Broglie’s equation = h/mv Can calculate the wavelength of an object. Can calculate the wavelength of an object.

Examples The laser light of a CD is 7.80 x 10 2 m. What is the frequency of this light? The laser light of a CD is 7.80 x 10 2 m. What is the frequency of this light? What is the energy of a photon of this light? What is the energy of a photon of this light? What is the apparent mass of a photon of this light? What is the apparent mass of a photon of this light? What is the energy of a mole of these photons? What is the energy of a mole of these photons?

What is the wavelength? Of an electron with a mass of 9.11 x kg traveling at 1.0 x 10 7 m/s? Of an electron with a mass of 9.11 x kg traveling at 1.0 x 10 7 m/s? Of a softball with a mass of 0.10 kg moving at 125 mi/hr? Of a softball with a mass of 0.10 kg moving at 125 mi/hr?

Diffraction Diffraction Grating splits light into its components of light of different frequencies or wavelengths. Diffraction Grating splits light into its components of light of different frequencies or wavelengths. When light passes through, or reflects off, a series of thinly spaced lines, it creates a rainbow effect When light passes through, or reflects off, a series of thinly spaced lines, it creates a rainbow effect Because the waves interfere with each other. Because the waves interfere with each other.

A wave moves toward a slit.

Comes out as a curve

with two holes

Two Curves

with two holes Interfere with each other

Two Curves with two holes Interfere with each other crests add up

Several waves

Several Curves

Several waves Interference Pattern Several Curves

Louis de Broglie ( ) Electrons should be considered waves confined to the space around an atomic nucleus

deBroglie “connected” the wave & particle natures of matter

deBroglie & Bohr consistent deBroglie started with

But, for constructive interference of a body orbiting in a circle

Which is Bohr Postulate #2

n = 2

n = 3

n = 5

Where: V = potential energy of electron E = total energy of electron  = wave function of electron Schroedinger Equation

For electron in ground state of hydrogen atom: (as a 1 st approximation) Where: r = distance electron from nucleus a o = Bohr radius

123123123123

122232122232122232122232 0 node 1 node 2 node

nucleus r

Distance from nucleus (pm) pm 22

Distance from nucleus (pm) 22

Heisenberg Uncertainty Principle

Quantum #s or QN ___, ___, ___, ___ n m l m s Electron Probability Space & Quantum Numbers

Principal QN = n n = 1, 2, 3,... ==> size and energy of orbital ==> relative distance of e - cloud from nucleus n = 1, 2, 3,... ==> size and energy of orbital ==> relative distance of e - cloud from nucleus for H: for H:

Principal QN = n for all other: for all other: where z = nuclear charge k = x joule

Angular Momentum QN = Shape of e- cloud corresponds/defines sub-level Shape of e- cloud corresponds/defines sub-level

Angular Momentum QN = nl # sub spectral 101 s 2 0,12 s, p 3 4 nl # sub spectral 101 s 2 0,12 s, p 3 4

Magnetic (orbital) QN = m l (m) u l m l 0 0 s-orbital

s - orbital

Magnetic (orbital) QN = m l (m) u l m l 0 0 s-orbital 1 -1,0,+1 (3) p-orbitals

p - orbital p x, p y, p z (3) px py pz

Magnetic (orbital) QN = m l (m) u l m l 0 0 s-orbital 1 -1,0,+1 (3) p-orbitals 2 -2,-1,0,+1,+2 (5) d-orbitals

d - orbitals (3) (1) (1) d xy, d yz, d xz

Spin QN = m s (s) spin of e - on own axis

max e - n = 1 max e - n = 1

max e - n = 1 s 2 n = 2 max e - n = 1 s 2 n = 2

max e - n = 1 s 2 n = 2 s 2 8 p 6 n = 3 max e - n = 1 s 2 n = 2 s 2 8 p 6 n = 3

max e - n = 1 s 2 n = 2 s 2 8 p 6 n = 3 s 2 p 6 18 d 10 max e - n = 1 s 2 n = 2 s 2 8 p 6 n = 3 s 2 p 6 18 d 10

max e - = 2n 2 n = 1 s 2 n = 2 s 2 8 p 6 n = 3 s 2 p 6 18 d 10 max e - = 2n 2 n = 1 s 2 n = 2 s 2 8 p 6 n = 3 s 2 p 6 18 d 10

Pauli Exclusion Principle nlm l s / / / / / /2 nlm l s / / / / / / / / / / / / / /2 Orbital 1S 2s 2p

Pauli Exclusion Principle No 2 e - in same atom can have the same set of four quantum numbers No 2 e - in same atom can have the same set of four quantum numbers

Quantum #s ___, ___, ___, ___ n m l m s Electron Probability Space & Quantum Numbers

Principal QN = n n = 1, 2, 3,... ==> size and energy of orbital ==> relative distance of e - cloud from nucleus n = 1, 2, 3,... ==> size and energy of orbital ==> relative distance of e - cloud from nucleus for H: for H:

Principal QN = n for all other: for all other: where z = nuclear charge k = x joule

Angular Momentum QN = Shape of e- cloud corresponds/defines sub-level Shape of e- cloud corresponds/defines sub-level

Angular Momentum QN = nl # sub spectral 101 s 2 0,12 s, p 3 4 nl # sub spectral 101 s 2 0,12 s, p 3 4

Magnetic (orbital) QN = m l (m) u l m l 0 0 (1) s-orbital

Magnetic (orbital) QN = m l (m) l m l 0 0 (1) s-orbital 1 -1,0,+1 (3) p-orbitals

Magnetic (orbital) QN = m l (m) u l m l 0 0 (1) s-orbital 1 -1,0,+1 (3) p-orbitals 2 -2,-1,0,+1,+2 (5) d-orbitals

Magnetic (orbital) QN = m l (m) u l m l 0 0 (1) s-orbital 1 -1,0,+1 (3) p-orbitals 2 -2,-1,0,+1,+2 (5) d-orbitals 3-3,-2,-1,0,+1,+2,+3 (7) f-orbitals